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A355635
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Triangle read by rows. Row n gives the coefficients of Product_{k=0..n-1} (x - binomial(n-1,k)) expanded in decreasing powers of x, with row 0 = {1}.
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0
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1, 1, -1, 1, -2, 1, 1, -4, 5, -2, 1, -8, 22, -24, 9, 1, -16, 93, -238, 256, -96, 1, -32, 386, -2180, 5825, -6500, 2500, 1, -64, 1586, -19184, 117561, -345600, 407700, -162000, 1, -128, 6476, -164864, 2229206, -15585920, 51583084, -64538880, 26471025
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OFFSET
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0,5
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COMMENTS
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Without signs the triangle of elementary symmetric functions of the terms binomial(n,j), j=0..n.
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LINKS
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FORMULA
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T(n, 0) = 1.
T(n, 1) = -2^(n-1), for n > 0.
T(n, 3) = -A025131(n-1), for n > 1.
T(n, n) = (-1)^n*A001142(n-1), for n > 0.
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EXAMPLE
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The triangle begins:
1;
1, -1;
1, -2, 1;
1, -4, 5, -2;
1, -8, 22, -24, 9;
1, -16, 93, -238, 256, -96;
1, -32, 386, -2180, 5825, -6500, 2500;
...
Row 4: x^4 - 8*x^3 + 22*x^2 - 24*x + 9 = (x-1)*(x-4)*(x-6)*(x-4)*(x-1).
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PROG
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(PARI) T(n, k) = polcoeff(prod(m=0, n, (x-binomial(n-1, m))), n-k+1);
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CROSSREFS
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Cf. A001142 (right diagonal unsigned).
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KEYWORD
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AUTHOR
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STATUS
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approved
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